Estimating correlation under interval uncertainty

doi:10.1016/j.ymssp.2012.12.003

Estimating correlation under interval uncertainty

2013-05-01

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Владик Крейнович *

DOI：10.1016/j.ymssp.2012.12.003

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In many engineering situations, we are interested in finding the correlation rho between different quantities x and y based on the values x(i) and y(i) of these quantities measured in different situations i. Measurements are never absolutely accurate; it is therefore necessary to take this inaccuracy into account when estimating the correlation rho. Sometimes, we know the probabilities of different values of measurement errors, but in many cases, we only know the upper bounds Delta(xi) and Delta(yi) on the corresponding measurement errors. In such situations, after we get the measurement results (x) over tilde (i) and (y) over tilde (i), the only information that we have about the actual (unknown) values x(i) and y(i) is that they belong to the corresponding intervals [(x) over tilde (i)-Delta(xi),(x) over tilde (i) + Delta(xi)] and [(y) over tilde (i)-Delta(yi),(y) over tildei + Delta(yi)] Different values from these intervals lead, in general, to different values of the correlation rho. It is therefore desirable to find the range [rho,(rho) over bar] of possible values of the correlation when x(i) and y(i) take values from the corresponding intervals. In general, the problem of computing this range is NP-hard. In this paper, we provide a feasible (=polynomial-time) algorithm for computing at least one of the endpoints of this interval: for computing (rho) over bar when (rho) over bar > 0 and for computing rho when rho <0. (c) 2012 Elsevier Ltd. All rights reserved.

Keyword:

Imprecise probabilities

Correlation

Interval uncertainity

Estimating correlation under interval uncertainty

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